Decays of Muons: Free and Bound
Continuing Advances in QCD Minneapolis, May 16, 2013
Andrzej Czarnecki University of Alberta
Outline
Free muon decay Theoretical vs experimental accuracy How to improve the theory
Lepton-flavor violation: searches Background: bound muon decay Modification of the electron spectrum by binding Precise description of the spectrum
Free muon decay
A model process in particle physics (tools for quark decays)
The first decay process known with one- and two-loop QED effects.
Anastasiou, Melnikov, Petriello, JHEP 0709 (2007) 014 van Ritbergen + Stuart, PRL 82 (1999) 488 Pak + Czarnecki, PRL 100 (2008) 241807
Also very thoroughly studied experimentally; most recently * decay distributions (“Michel parameters”) TWIST PRD 85 (2012) 092013 * total rate (1 ppm!) MuLan PRL 106 (2011) 041803
Fermi constant and tests of the SM
Determination of the Fermi constant (convention)
Muon lifetime in Fermi theory, with QED
Pak, AC
Example: electron vacuum polarization
How well can the muon lifetime be measured?
Theoretical accuracy of the muon decay rate
Can the three loop effect be determined?
We have found an interesting way while checking the two-loop result: the calculation would be easier if the electron was very heavy, almost as heavy as the decaying muon.
Expansion around the equal mass limit with M. Dowling and M. Czakon
Electron and muon masses: the only characteristic scales.
We are interested in the limit
The imaginary part of five-loop integrals needed; no contribution when all loop momenta “hard” (this simplifies the task – a lot).
Estimate of the three-loop coefficient
The NNNLO axial formfactor is known in the zero-recoil limit.
It determines the first two orders in the mass expansion (real radiation more strongly suppressed).
NLO NNLO
NNNLO
Another application of the muon lifetime
Muons and antimuons behave differently in matter. Negatively-charged muons form muonic atoms and can be captured by nuclei. o k
n The rate of capture, e h c h
s found from the lifetime i T . V difference, determines nucleon formfactors.
Lepton-flavor violating processes and the muon decay in orbit
Muon g-2: ~3.6σ discrepancy
Encouragement for lepton flavor violation searches:
New bound (MEG @ Paul Scherrer Institute) probes
(Also lots of theoretical encouragement from “new physics” models.)
Muon-electron conversion
“The best rare process” No accidental bkgd (single monochromatic e-); 10-17 sensitivity envisioned
Variety of mechanisms:
Comparison with scattering experiments
Highest luminosity in fixed-target experiments
In a single muonic atom
Comparison with scattering experiments
Highest luminosity in fixed-target experiments
In a single muonic atom
Muon decay in orbit (DIO)
Background from the standard muon decay
neutrinos electron
Background from the standard muon decay
End point spectrum must be well understood
End point spectrum
Previous studies: Shanker & Roy, Hänggi et al., Herzog & Alder
Relativistic muon wave function, nuclear size and recoil, electron final state interactions: all taken into account.
New evaluation: AC, X. Garcia i Tormo, W. J. Marciano PRD84,013006,2011
Planned energy resolution in Mu2e: ~250 keV 0.22 background events.
How can the electron get muon’s whole energy?
Neutrinos get no energy; The nucleus balances electron’s momentum, takes no energy. Near the end point:
µ-e conversion may be caused by a majoron
What is the majoron?
If neutrinos have Majorana masses: lepton number is not conserved.
How can lepton conservation be broken? * explicitly by the Majorana mass term; * spontaneously, locally; or * spontaneously, globally Goldstone boson.
Majoron can violate lepton flavor number
The resulting extra muon decay rate:
What is the electron spectrum in µe+J ?
Free muon: monoenergetic electron, Ee = mµ/2 o m r o Muon bound in an atom: spread out up to mµ T i a i c r a G
. X
, g n i l w o D
. M
, n a m y r B
. D h t i W
Vanishes at end point Results: electron spectrum in µ e+J n o r f a z S t r e b o R
without binding effects, the electron spectrum is monochromatic, concentrated here at half muon mass
Results: electron spectrum in µ e+J n o r f a z S t r e b o R
smearing due to expansion muon's motion. in Z*alpha Dominates in the center. Correct far from the center
Summary
We have determined spectra of daughter electrons in decays of bound muons. Simple interpretation of the high-energy tail: hard photon exchange with the nucleus.
The signal of possible decays into majorons is enhanced by two powers of
(Emax - Ee) but not by four powers.
Ongoing work: better understanding of the muon decay in orbit: an effective theory approach to various regions of the spectrum (with R. Szafron).
Lepton-flavor violating processes and the muon decay in orbit
Why such a large correction?
Difference between the normal muon decay and the eγ channel
dimension=4, renormalizable dimension=5, non-renormalizable: large logs in the photon loops
Other processes, and the conversion,
have a mixture of both structures. Large logs can be present.